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If x ,1,a n dz are in A.P. and x ,2,a n ...

If `x ,1,a n dz` are in A.P. and `x ,2,a n dz` are in G.P., then prove that `x ,a n d4,z` are in H.P.

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To prove that \( x, 4, z \) are in Harmonic Progression (H.P.) given that \( x, 1, z \) are in Arithmetic Progression (A.P.) and \( x, 2, z \) are in Geometric Progression (G.P.), we can follow these steps: ### Step 1: Use the property of A.P. Since \( x, 1, z \) are in A.P., the middle term is the arithmetic mean of the other two terms. Therefore, we have: \[ 1 = \frac{x + z}{2} \] Multiplying both sides by 2 gives: ...
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